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A244857

Numbers divisible by both the sum of the squares of their digits and the product of their digits.

1, 111, 315, 1344, 3312, 4416, 6624, 11112, 12312, 31311, 114192, 121716, 134112, 134136, 141312, 231336, 282624, 313416, 314112, 411648, 431136, 613116, 628224, 1112232, 1112832, 1121232, 1122112, 1122312, 1122912, 1143216, 1211232, 1212112, 1212192, 1212312

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OFFSET

1,2

COMMENTS

Subsequence of A034087.

The property "numbers divisible by the sum of the squares and product of their digits" leads to the Diophantine equation t*x1*x2*...*xr=s*(x1^2+x2^2+...+xr^2), where t and s are divisors of n; xi is from [1...9].

Intersection of A034087 and A007602. - Jens Kruse Andersen, Jul 13 2014

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000

EXAMPLE

315 is in the sequence because 3^2+1^2+5^2 = 35 divides 315 and 3*1*5 = 15 divides 315.

MATHEMATICA

dspQ[n_]:=Module[{idn=IntegerDigits[n], t}, t=Times@@idn; t!=0 && Divisible[n, Total[idn^2]] && Divisible[n, t]]; Select[Range[2*10^6], dspQ]

PROG

(PARI) isok(n) = (d = digits(n)) && (prd = prod(i=1, #d, d[i])) && !(n % prd) && !(n % sum(i=1, #d, d[i]^2)); \\ Michel Marcus, Jul 07 2014

CROSSREFS

Cf. A007602, A034087, A038186, A117562.

Sequence in context: A271312 A171773 A349951 * A225329 A277960 A304831